Tan 15° – Tan15° Value – What is the tan of 15 degrees? (2024)

Welcome to tan 15°, our post aboutthe tangent of 15 degrees.

For the tangent of 15 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 15°.

If you have been looking for what is tan 15°, or if you have been wondering about tan 15 degrees in radians, then you are right here, too.

In this post you can find the tan 15° value, along with identities.

Read on to learn all about the tan of 15°.

Tan 15 Degrees

If you want to know what is tan 15 degrees in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of tan 15°:

The tan of 15 degrees is 2-√3, the same as tan of 15 degrees in radians. To obtain 15 degrees in radian multiply 15° by $\pi$ / 180° = 1/12 $\pi$. Tan 15degrees = tan (1/12 × $\pi)$.

Our results of tan15° have been rounded to five decimal places. If you want tangent 15° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate tan 15 degrees insert the angle 15 in the field labelled °, but if you want to calculate tan 15 in radians, then you have to press the swap unit button first.

A Really Cool Tangent Calculator and Useful Information! Please ReTweet. Click To TweetBesides tan15°, similar trigonometric calculations on our site include, but are not limited, to:

• Tan -4.51
• Tg -6.08
• Tg 1.35

The identities of tangent 15° are as follows:

Note that tan15° is periodic: tan (15° + n × 180°) = tan 15 degrees, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × 15°), half angle ((15/2)°) as well as the sum, difference and products of two angles such as 15° and β.

You can locate all of them in the respective article found in the header menu. To find everything about tan -15° click the link. And here is all about cot 15°, including, for instance, a converter.

In terms of the other five trigonometric functions, tan of 15° =

• $\pm\frac{\sin 15^\circ}{\sqrt{1 – \sin^{2} 15^\circ}}$
• $\pm\frac{\sqrt{1 – \cos^{2} 15^\circ}}{\cos 15^\circ}$
• $\pm \sqrt{\sec^{2} 15^\circ -1}$
• $\pm\frac{1}{\sqrt{\csc^2 15^\circ – 1}}$
• $\frac{1}{\cot 15^\circ}$

As the cotangent function is the reciprocal of the tangent function, 1 / cot 15° = tan15°.

In the next part of this article we discuss the trigonometric significance of tan15°, and there you can also learn what the search calculations form in the sidebar is used for.

What is tan 15°?

In a triangle which has one angle of 90 degrees, the tangent of the angle of 15° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 15° = o/a.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 15 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

Applying the unit-circle definition found on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, y = sin 15°, x = cos 15° and tan 15° = sin 15°/cos 15°.

Bringing together the triangle definition and the unit circle definition of tangent 15 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 15^\circ$.

Note that you can locate many terms including the tangent15° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan15°.

Along the same lines, using the aforementioned form, can you look up terms such as tan 15° value, tan 15, tan15° value and what is the tan of 15 degrees, just to name a few.

Given the periodicity of tangent of 15°, to determine the tangent of an angle > 180°, e.g. 735°, calculate tan 735° as tan (735 Mod 180)° = tangent of 15°, or look it up with our form.

Conclusion

The frequently asked questions in the context include what is tan 15 degrees and what is the tan of 15 degrees for example; reading our content they are no-brainers.

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– Article written by Mark, last updated on February 26th, 2017